1. 集合记号¶

1.1. 集合入门¶

数学意义上的集合概念在计算机科学中有广泛的应用。集合论的记号与技巧常用于描述和实现算法，因为与集合相关的抽象往往有助于澄清和简化算法设计。因此，掌握这套记号有助于你与其他计算机科学家交流。

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1.2. 集合的常用记号¶

下表列出常用于表示集合并表达其关系的符号。

Table 2.1.1 )

\[\begin{split}\begin{array}{l|l} \{1, 4\}& \mbox{A set composed of the members 1 and 4}\\ \{\mathsf{x}\, |\, \mathsf{x}\ \mbox{is a positive integer}\}& \mbox{A set definition using a set former}\\ &\qquad \mbox{Example: the set of all positive integers}\\ \mathsf{x} \in \mathbf{P}&\mathsf{x}\ \mbox{is a member of set}\ \mathbf{P}\\ \mathsf{x} \notin \mathbf{P}&\mathsf{x}\ \mbox{is not a member of set}\ \mathbf{P}\\ \emptyset&\mbox{The null or empty set}\\ |\mathbf{P}|& \mbox{Cardinality: size of set}\ \mathbf{P} \mbox{or number of members for set}\ \mathbf{P}\\ \mathbf{P}\,\subseteq\,\mathbf{Q}, \mathbf{Q}\,\supseteq\,\mathbf{P}& \mbox{Set}\ \mathbf{P}\ \mbox{is included in set}\ \mathbf{Q},\\ &\qquad \mbox{set}\ \mathbf{P}\ \mbox{is a subset of set}\ \mathbf{Q},\\ &\qquad \mbox{set}\ \mathbf{Q}\ \mbox{is a superset of set}\ \mathbf{P}\\ \mathbf{P}\,\cup\,\mathbf{Q} & \mbox{Set Union: all elements appearing in} \ \mathbf{P}\ \mbox{OR}\ \mathbf{Q}\\ \mathbf{P}\,\cap\,\mathbf{Q} & \mbox{Set Intersection: all elements appearing in}\ \mbox{P} \ \mbox{AND}\ \mathbf{Q}\\ \mathbf{P}\,-\,\mathbf{Q} & \mbox{Set difference: all elements of set} \ \mathbf{P}\ \mbox{NOT in set}\ \mathbf{Q}\\ \mathbf{P}\,\times\,\mathbf{Q} & \mbox{Set (Cartesian) Product: yields a set of ordered pairs}\\ \end{array}\end{split}\]